A new multistage swash plate piston gas pump is proposed. According to the structural characteristics of the two-side swash plate gas pump and the law of relative motion of its pistons, multistage compression could be achieved by dividing the cylinders into several levels and connecting the cylinders at the same level in parallel and the cylinders at the adjacent level in series with check valve rectifying in the front and back cylinder cover.The structural characteristics and working principles of the gas pump were elaborated. The kinematic characteristics of the gas pump were analyzed and calculated. Mathematical model of gas compression and expansion thermal process for the gas pump was established and the fourth order Runge-Kutta numerical method was used to solve it. The thermodynamic characteristics of the gas pressure and temperature in the work process of the gas pump were analyzed. Furthermore, the advantages of the multistage compression with respect to the single-stage compression are comparatively analyzed from two aspects of saving the indicated work of the compressed gas and reducing exhaust temperature.